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Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

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 نشر من قبل Adrian Vasiu
 تاريخ النشر 2020
  مجال البحث
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 تأليف Adrian Vasiu




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We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic $(0,p)$ of integral canonical models of projective Shimura varieties of Hodge type with respect to h--hyperspecial subgroups as pro-etale covers of Neron models; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.



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